Two-dimensional Dipole Systems Research Articles

Shear viscosity in two-dimensional dipole systems.

The results of modeling shear flows in classical two-dimensional (2D) dipole systems are presented. We used the method of nonequilibrium molecular dynamics to calculate the viscosity at various shear rates. The coefficients of shear viscosity are given in the limit of low shear rates for various regimes of interparticle correlation from a weakly correlated gaseous state to a strongly nonideal liquid state near the crystallization point. The calculations were carried out for bare (unscreened) dipole systems, as well as for dipole systems in a polarizable medium that provide screening of the dipole-dipole interaction. The effect of shear thinning in 2D dipole systems is reported for low values of the coupling parameter. In addition, it is shown that dipole systems can become both less and more viscous due to the presence of a screening medium, depending on the degree of interparticle correlation. The optimal simulation parameters are discussed within the framework of the method of nonequilibrium molecular dynamics for determining the shear viscosity of two-dimensional dipole systems. Moreover, we present a simple fitting curve which provides a universal scaling law for both bare dipole-dipole interaction and screened dipole-dipole interaction.

Melting, freezing, and dynamics of two-dimensional dipole systems in screening bulk media.

This paper reports on the molecular dynamics simulations of classical two-dimensional (2D) electric dipole systems. The properties of 2D systems with bare (nonscreened) and screened dipole-dipole interactions have been investigated. Based on the polygon construction method, we present simulation results on the phase transition, and we locate the melting and freezing points of 2D dipole systems in terms of a polygon disorder parameter, with the polygon disorder parameter being the sum of nontriangular polygon order parameters. It was found that the phase transition of the system occurs when the polygon disorder parameter has a value 0.165. This result was cross-checked by using both local and overall orientational order parameters. We also identified that the value of the average local orientational order parameter at the phase transition point is 0.67. These results are valid for the ordinary (bare) dipole-dipole interaction as well as the screened dipole-dipole interaction, and they are expected to be general for other 2D systems with repulsive pair interaction. We observed that both melting and freezing points shift to lower values of temperature due to screening. In the liquid state, the radial distribution function and polygon construction method show the loss of order in a structure as screening becomes more severe. Furthermore, the impact of screening on the system's collective excitation spectra and diffusive characteristics at liquid and solid states has been studied. Results show the decrease in the values of both longitudinal and transverse sound speeds and the emergence of anomalous superdiffusive motion in the liquid state due to screening.

The structure and spectral properties of two-dimensional dipole systems

A molecular dynamics simulation of two-dimensional dipole systems was performed. The influence of particles dipole moment (PDM) on structures and spectral properties of the systems was analyzed. It was found that increase of PDM leads to qualitative changes in systems structure and spectrum. There is a critical ratio between temperature and PDM at which the system is polymerized. It was also shown that the spectral properties of the system are extremely sensitive to PDM.

Dynamics of two-dimensional dipole systems

Using a combined analytical/molecular dynamics approach, we study the current fluctuation spectra and longitudinal and transverse collective mode dispersions of the classical two-dimensional (point) dipole system (2DDS) characterized by the ϕ{D}(r)=μ{2}/r{3} repulsive interaction potential; μ is the electric dipole strength. The interest in the 2DDS is twofold. First, the quasi-long-range 1/r{3} interaction makes the system a unique classical many-body system, with a remarkable collective mode behavior. Second, the system may be a good model for a closely spaced semiconductor electron-hole bilayer, a system that is in the forefront of current experimental interest. The longitudinal collective excitations, which are of primary interest for the liquid phase, are acoustic at long wavelengths. At higher wave numbers and for sufficiently high coupling strength, we observe the formation of a deep minimum in the dispersion curve preceded by a sharp maximum; this is identical to what has been observed in the dispersion of the zero-temperature bosonic dipole system, which in turn emulates so-called roton-maxon excitation spectrum of the superfluid 4He . The analysis we present gives an insight into the emergence of this apparently universal structure, governed by strong correlations. We study both the liquid and the crystalline solid state. We also observe the excitation of combination frequencies, resembling the roton-roton, roton-maxon, etc. structures in 4He .

Collective excitations in a two-dimensional dipole system

We address the question of collective excitations in two-dimensional (2D) dipolar systems. The main issue is that such systems have no Hartree and no random-phase-approximation (RPA) limits and calculations have to include particle correlations from the outset. We focus on the longitudinal collective mode representing the density oscillations of the dipoles and on the transverse collective mode representing shear waves. Our theoretical approach is based on the quasi-localized charge approximation (QLCA) adapted to point-dipole systems interacting through a 1/r3 potential. Our analytical calculation is accompanied by classical molecular dynamics (MD) simulation. At long wavelengths, the longitudinal and transverse collective excitations exhibit acoustic behaviors with phase velocities that vary linearly with the dipole strength and are wholly maintained by particle correlations. At finite wavenumbers, the mode dispersion resulting from our classical MD simulations shows a roton-like behavior. Comparison with the quantum Monte Carlo dispersion generated through the Feynman relation (Astrakharchik et al 2007 Phys. Rev. Lett. 98 060405) shows a remarkably good quantitative agreement between the two.

Erratum: Acoustic dispersion in a two-dimensional dipole system [Phys. Rev. B78, 045304 (2008)

Received 11 December 2008DOI:https://doi.org/10.1103/PhysRevB.78.239905©2008 American Physical Society

Acoustic dispersion in a two-dimensional dipole system

We calculate the full density response function and from it the long-wavelength acoustic dispersion for a two-dimensional system of strongly coupled point dipoles interacting through a $1/{r}^{3}$ potential at arbitrary degeneracy. Such a system has no random-phase-approximation (RPA) limit and the calculation has to include correlations from the outset. We follow the quasilocalized charge (QLC) approach, accompanied by molecular-dynamics (MD) simulations. Similarly to what has been recently reported for the closely spaced classical electron-hole bilayer [G. J. Kalman et al., Phys. Rev. Lett. 98, 236801 (2007)] and in marked contrast to the RPA, we report a long-wavelength acoustic phase velocity that is wholly maintained by particle correlations and varies linearly with the dipole moment $p$. The oscillation frequency, calculated both in an extended QLC approximation and in the Singwi-Tosi-Land-Sjolander approximation [Phys. Rev. 176, 589 (1968)], is invariant in form over the entire classical to quantum domains all the way down to zero temperature. Based on our classical MD-generated pair distribution function data and on ground-state energy data generated by recent quantum Monte Carlo simulations on a bosonic dipole system [G. E. Astrakharchik et al., Phys. Rev. Lett. 98, 060405 (2007)], there is a good agreement between the QLC approximation kinetic sound speeds and the standard thermodynamic sound speeds in both the classical and quantum domains.

Striped phases in two-dimensional dipole systems

We prove that a system of discrete 2D in-plane dipoles with four possible orientations, interacting via a 3D dipole-dipole interaction plus a nearest neighbor ferromagnetic term, has periodic striped ground states. As the strength of the ferromagnetic term is increased, the size of the stripes in the ground state increases, becoming infinite, i.e., giving a ferromagentic ground state, when the ferromagentic interaction exceeds a certain critical value. We also give a rigorous proof of the reorientation transition in the ground state of a 2D system of discrete dipoles with six possible orientations, interacting via a 3D dipole-dipole interaction plus a nearest neighbor antiferromagnetic term. As the strength of the antiferromagnetic term is increased the ground state flips from being striped and in-plane to being staggered and out-of-plane. An example of a rotator model with a sinusoidal ground state is also discussed.

Orientational states, phase transitions, and spectra of vibrational excitations for two-dimensional systems with quadrupole interactions

Consideration concerns a two-dimensional system of molecules fixed by an adsorption potential at lattice sites of a square lattice at a definite angle θ to the surface normal. Among lateral intermolecular interactions including quadrupole, dispersion, and repulsive, the former are regarded as predominating. At small θ, the Hamiltonian of the system is shown to reduce to that of the thoroughly studied two-dimensional dipole system with renormalized interaction constants. The hierarchy of ground-state orientational phases depending on the angle θ is established in two particular cases: for free azimuthal rotation and for four discrete orientations of projections of long molecular axes along square-lattice axes. The latter case is included in the diagram of temperature phase transitions. The results obtained adequately describe the properties of the 2×1 phase of CO/NaCl(100). The structure of the observed ground state and the orientational phase transition temperature are reproduced correctly. The spectrum of orientational vibrations calculated for this system is characterized by the band half-width which is consistent in the order of magnitude with those found from experimental temperature dependences of spectral line shifts and widths for local C–O vibrations dephased on orientational vibrations.

Quantum crystallization of two-dimensional dipole systems

An analysis is made of the region of existence of crystalline order in a system of spatially separated electrons (e) and holes (h) in two coupled quantum wells for various concentrations n, temperatures T, and distances D between the layers. A study is also made of crystallization in a system of electrons in semiconductor structures near a metal electrode for various distances d between the semiconductor and the metal. Calculations of the crystalline phase were made using variational calculations of the ground-state energy of the system allowing for pairing of quasiparticles with nonzero momentum. For a system of two coupled quantum wells, regions in (T,n,D) space are determined in which electron (or hole) charge-density waves exist in each layer and regions where these charge-density waves are in phase, in other words, indirect excitons (or pairs with spatially separated electrons and holes) interacting as electric dipoles, become crystallized. In the electron system in semiconductor structures near a metal electrode, regions of existence of an electron crystal are also obtained in (T,n,D) space, where over large distances the electrons interact as electric dipoles because of image forces.

Dephasing of local vibrations of a two-dimensional dipole system

Anharmonically coupled, high-and low-frequency branches of vibrational excitations of a two-dimensional dipole system on a substrate are studied. It is shown that independent low-frequency resonance modes characterized by a two-dimensional wave vector belonging to the first Brillouin zone of the dipole lattice arise as a result of the harmonic interaction of phonons in the dipole system and in the substrate. The positions and widths of the spectral lines of the high-frequency local vibrations, which in the general case depend on the dispersion laws and lifetimes of the resonance modes, are calculated for low-temperature orientational states of degenerate dipoles on triangular and square lattices.

Long-range order in a classical two-dimensional dipole system

A two-dimensional system of classical dipoles on a triangular lattice with isotropic in-plane ordering is studied both in the spin-wave approximation and by Monte-Carlo simulation. It is shown that the mean-square displacement ( theta 2), unlike in the two-dimensional XY model, is finite in this system in the thermodynamic limit-not divergent logarithmically. This boundedness of ( theta 2) is caused, as demonstrated, by the long-range nature of the potential.

Vibrational spectra of surface hydroxyl groups in various phases including dipole glass

Experimental data are discussed, suggesting thermally activated reorientations of OH(D) groups on the silica surface. The orientation phases are calculated for a two-dimensional dipole system on the trigonal lattice with disordered point filling. The results presented also concern the reorientation widening of the spectral bands and their general structure in the paraelectric phase, as well as basic parameters of vibrational spectra in ferroelectric and dipole glass phases. The theoretical estimates are in good agreement with the spectroscopic evidence.

Vibrational and orientational states of surface atomic groups

This survey is devoted to the current state of theoretical studies of two-dimensional dipole systems. Systems of hydroxyl groups on the surfaces of oxides have been the most experimentally studied systems. The article examines the orientational states of isolated radicals in local potentials of hindered rotation, various types of orientational ordering of dipoles in twodimensional lattices, and the appearance of the dipole glass phase in a system with arbitrary filling of lattice sites by particles. Proof is presented of the existence of long-range order in twodimensional dipole systems, as well as estimates of phase transition temperatures. There is a discussion of the theory of the vibrational spectra of ordered and disordered systems of dipole radicals in various orientational phases. Experimental data are presented on the infrared spectroscopy of surface hydroxyl groups. The data verify theoretical results. Unresolved problems are indicated as well as the prospects for further studies of two-dimensional dipole systems.

Oreintation vibrations in two-dimensional dipole systems

A general theory is developed for low temperature orientations vibrations of dipoles on arbitrary two-dimensional Bravais lattices with any anisotropic interactions. The theory involves a method for calculating the dipole system ground state, as well as the analysis of its properties and stability (i.e. long-range order) with respect to the relatively longwave angular fluctuations. Specific results are obtained for the dipole-dipole potential. In particular, dipole orientation vibrations about the stable ferroelectric ground state on a trigonal lattice are shown to display a non-trivial asymptotic behaviour of frequency distribution g(ω) at low frequencies and specific heat c(T):g(ω)∼ω 3/2 ; c(T)∼T 5/2